Question

Consider an infinite surface charge in y-z plane with density σ. Electric field at any point in positive x-axis is σ/2ϵ (i hat) and electric field at any point in negative x-axis is -σ/2ϵ (i hat). Thus we see there is a discontinuity of σ/ϵ at the surface (at x=0). What will be the electric field on the surface charge? That is, what will be the electric field at x=0?

Answer 1

What will be the electric field on the surface charge?

$$E=\frac {\sigma} {2ɛ}$$

what will be the electric field at x=0?

$$E=\frac {\sigma} {2ɛ} - \frac {\sigma} {2ɛ}=0$$